Quaternions
Quaternions are a number system that extends complex numbers, represented as a + bi + cj + dk, where a, b, c, d are real numbers and i, j, k are fundamental quaternion units with specific multiplication rules. They are widely used in computer graphics, robotics, and physics to represent 3D rotations and orientations without suffering from gimbal lock, a problem common with Euler angles. Quaternions provide an efficient and numerically stable way to interpolate between rotations, such as in animation or game development.
Developers should learn quaternions when working on 3D applications, such as video games, simulations, or augmented/virtual reality, where smooth and accurate rotation handling is critical. They are essential for avoiding gimbal lock in Euler angles and for performing spherical linear interpolation (SLERP) to create natural animations. In fields like robotics and aerospace, quaternions are used for attitude control and sensor fusion due to their compact representation and computational advantages over rotation matrices.